As promised here are some observational data that show the improvement in signal-to-nose with a cross-correlation. Here’s a spectrogram of the bird call:
The data I’m gong to look at here are 0.15 sec in duration starting at 0.61 sec. I’ve taken a quiet period to estimate the background noise and then calculated SNR for single microphones, an average and the cross correlation. The first plot shows SNR against frequency:
There’s more scatter in the SNR estimates for cross-correlation because the noise levels are so much lower and therefore more poorly measured! Nevertheless, the SNR is clearly higher where there is signal. Possibly a better way to show this is to look at SNR against signal strength (similar to the last plot shown in the previous blog entry)::
Again, there’s more uncertainty in the SNR estimates for cross-correlation but it’s clear that signals can be detected to a lower level and with higher SNR than the other methods.
If we take a required detection SNR of 10 for example, the signal strength that can be detected with the cross correlation technique is a factor of about 2.7 weaker than a single microphone. This corresponds to a factor of 1.6 increase in range for the detector (or 2.7 in area or 4.4 in volume). By comparison, summed data give a factor of 1.2 improvement in range (1.4 in area, 1.7 in volume).